Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C83 · Schur multiplier (H2) = C2 |
| direct product | #333×C83 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C83 | C22⋊C4 |
| commutator | C2×C4 | C2×C4×C83 |
| Frattini, cosocle | C42 | C22×C83 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C42×C83 ◁ G | |
64 conjugacy classes of subgroups.
1577 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×#1405, C2×#333×C83, C83×#1542, … |
| maximal normal subgroup of | C83×#1405, C2×#333×C83, C83×#1542, … |
| maximal quotient of | C83×#1272, C83×#1296, C83×#1366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 14);